Various approaches describe the integration of silicon-based image sensors measuring intensity, amplitude and phase of an incident electro-magnetic wave front in the optical spectrum (e.g., WO-96/15626). These optical phase-measurement techniques can be used in optical range sensing. In combination with a dedicated light source, the pixel can be used as time-of-flight (TOF) ranging system (cf. EP-1′152′261 A) and/or in chemical and bio-chemical sensing (cf. EP-1′085′315 A). Homodyne signal detection systems are characterized by demodulating the incoming signal with the same base frequency of the reference signal. Hence, in homodyne optical TOF ranging systems, the active illumination source is synchronized with the driving signal of various photo gates, which leads to an information-carrying signal content at DC (f=0) and which in turn can be directly converted to digital values by appropriate analog-to-digital converters (ADCs) in modern information-processing systems. On the other hand, in heterodyne systems, the frequency of the light source differs slightly from the gate-controlling reference frequency and hence avoids potential problems with DC drift over power supply and temperature variations in practical implementations. This approach is characterized by the fact that the information-carrying part of the signal is hidden in the frequency content of the signal and has to be extracted by appropriate time-domain or frequency-domain analysis. In both cases, however, the signal of the incident optical wave front is demodulated by generating appropriate electrical fields in the gate-controlled silicon area of the sensor.
The electrical field is in most cases controlled by some applied voltage at the sensor input. In this region exhibiting commonly a stair-cased or linear potential gradient, the photo-generated electrons tend to drift towards the region in the semiconductor with the highest (deepest) potential well due to the electrical field created within the semiconducting material. By appropriately controlling the gates, the photo-generated charge carriers can be directed into the different integration gates or read-out nodes. From the resulting output signals, the characteristics of the incoming wave front can then be derived immediately.
A commonly used implementation is to provide a pixel with four outputs and to direct the photo-generated charge carriers to each output during one quarter of the full period of the incoming optical wave. The phase can be deduced from the four outputs corresponding to the relative phases 0°, 90°, 180° and 270° according to:
                              Phase          ⁢                                          ⁢          φ                =                              tan                          -              1                                ⁡                      (                                                            output                  ⁢                                                                          ⁢                  0                                -                                  output                  ⁢                                                                          ⁢                  180                                                                              output                  ⁢                                                                          ⁢                  270                                -                                  output                  ⁢                                                                          ⁢                  90                                                      )                                              (        1        )            
At the same time, the simplified equations for the amplitude and the intensity values become:
                              Amplitude          ⁢                                          ⁢          A                =                                                                              (                                                            output                      ⁢                                                                                          ⁢                      0                                        -                                          output                      ⁢                                                                                          ⁢                      180                                                        )                                2                            +                                                (                                                            output                      ⁢                                                                                          ⁢                      90                                        -                                          output                      ⁢                                                                                          ⁢                      270                                                        )                                2                                              2                                    (        2        )                                          Intensity          ⁢                                          ⁢          B                =                                            output              ⁢                                                          ⁢              0                        +                          output              ⁢                                                          ⁢              90                        +                          output              ⁢                                                          ⁢              180                        +                          output              ⁢                                                          ⁢              270                                4                                    (        3        )            
One of the main problems of state-of-the-art implementations of such systems, either homodyne systems such as described in the above-mentioned 4-outputs example or heterodyne phase measurement methods, appears as soon as the different output signal paths do not behave identically at constant illumination levels. These non-idealities might be caused by mismatch effects at the solid-state imager level and in the complementary metal-oxide semiconductor active-pixel sensor (CMOS APS) read-out path as well as with the non-ideal driving controls of the gates. As can be seen from Equations (1) and (2), the calculations are based on difference values, which can be severely affected by different offset or gain values.